Not having heard the phrase and finding no reference in the usual explanatory sites, I
can explain that Norman Rockwell was a famous and successful artist that documented everyday life in unusual ways within the U.S., centered on the era of about 1920 to, perhaps 1960. All his art had a
down-homey feel that everyone immediately recognized as, well, next doorish. Since, I expect that a chestnut-stuffed turkey is old fashioned and could easily be compared to the type of art work Mr. Rockwell produced I can see the comparison as being somewhat complimentary with the intent of implying commoness...
In case you're unfamiliar with Rockwell, here's a link for examples:
http://www.rockwellsite.com/prints/pag_images_ cl.asp?SE=CL&PG=